A research program, involving 3 British universities, directed at quantifying the controllability of High Temperature Superconducting (HTS) magnets for use in attraction levitation transport systems will be described. The work includes measurement of loss mechanisms for iron cored HTS magnets which need to produce a flux density of approx. 1 tesla in the airgap between the magnet poles and a ferromagnetic rail. This flux density needs to be maintained and this is done by introducing small variations of the magnet current using a feedback loop, at frequencies up to 10 Hz to compensate for load changes, track variation etc. The test magnet assemblies constructed so far will be described and the studies and modelling of designs for a practical levitation demonstrator (using commercially obtained HTS tape) will be discussed with particular emphasis on how the field distribution and its components, e.g., the component vector normal to the broad face of the tape, can radically affect design philosophy compared to the classical electrical engineering approach. Although specifically aimed at levitation transport the controllability data obtained have implications for a much wider range of applications.